That's the question some are asking as the detail's longtime head, Deputy Inspector Charles Dunne, retires and Bloomberg seeks to replace him with the detail's lieutenant, John Brennan.

If you're a betting man, you'd be wise to choose the mayor.

There are two theories -- rumors, some might say -- on Kelly's attitude about this: He is merely annoyed, or downright furious that Bloomberg has pre-empted him.

On one point, however, everyone agrees: Kelly is too smart and too disciplined to complain in public.

Mayoral details are one of the few areas - perhaps the only area -- where Bloomberg has pushed back against the police commissioner, to whom he has given more power than any other in the city's history.

In 2002 when Bloomberg became mayor and Rudy Giuliani was still viewed as the hero of 9/11, Bloomberg ordered Kelly to provide the former mayor with a permanent police detail.

For the next 18 months, Kelly assigned up to two dozen detectives to protect Rudy, his wife, two children, his mother and his then-mistress, Judy Nathan.

Kelly was a good soldier but he was not a happy camper. It wasn't merely that he recognized -- more clearly than Bloomberg did -- that Giuliani, now a private citizen with a multi-million dollar income, could afford to pay for his own private security.

More importantly, Kelly resented Giuliani for having dismissed him -- a David Dinkins appointee -- as police commissioner when Giuliani became mayor in 1994.

When Bloomberg ended Giuliani's detail a year later, Kelly took his revenge.

Powerless against Giuliani, he retaliated against the detail's detectives, whose lives he controlled.

He transferred some of the detectives to assignments as far from their homes as possible. For example, he reassigned two detectives who lived in Staten Island to the farthest reaches of Manhattan and the Bronx.

But Kelly's revenge was short-lived. After hearing from Giuliani, Bloomberg ordered Kelly to reassign them closer to home. Openings for the two Staten Island detectives materialized in the local District Attorney's office of William Murphy. Murphy, a Democrat, had defeated Guy Molinari, a Republican, in the last DA's race. Kelly had publicly supported Molinari.

As for the current detail, D.I. Dunne is becoming a federal marshal, no doubt because of Bloomberg's backing. As for Brennan, he is the equivalent of NYPD royalty, of the Brooklyn-based Brennan clan. His father, Paddy Brennan, was a two-star chief. His late brother Dermot continued to serve the NYPD for 12 years after he was diagnosed with brain cancer and underwent a series of operations, chemotherapy and radiation. In December, 2002, five days after yet another surgery, which left his arm and leg partially paralyzed, he walked across the stage at Police Plaza to receive his final promotion, to first grade detective.

So Brennan will continue to accompany the mayor on his weekend jaunts to Bermuda, which are becoming controversial, which may explain why Mayor Mike wants someone at his side whom he knows and trusts, not someone appointed by Kelly.

The Timesreported last week that Bloomberg travels to Bermuda with two officers who have special permission to carry weapons, which are largely forbidden in Bermuda. Meanwhile, the island's Ministry of Home Affairs denies the mayor comes with armed guards.

As the department's official unofficial historian Mike Bosak put it: Who would you believe, the Bermuda Home Ministry or the Times?

The Times also reported that Bloomberg "has walled off his life in Bermuda from voters in New York, arguing it is none of their business," and hosts "small parties at his house [where] ... gardeners have stopped trimming the vegetation ... [and] now largely blocks the view from the water."

No doubt Bloomberg feels he can continue to count on his detail's discretion and ensure that no one videotapes his weekend soirees.

POLICE TRIALS. Judge Jack Weinstein's courtroom in Brooklyn federal court seemed like Police Central last week. First came a 12-man jury's decision clearing four cops - Officers Young Yoo and Stephen Viani, Sgt. Pete Alfano and off-duty detective Leonard Ciurcina -- of conspiracy charges in their 2005 arrest of Aaron Wong. Wong, a young black man from Staten Island, had his jaw broken by a retired white detective, James Mangone, who was not arrested.

The same jury found Mangone guilty of discriminating against Wong and ordered him to pay $200,000 in compensatory and punitive damages. The incident apparently did not hurt the careers of Yoo and Viani, who have since been promoted to sergeant.

Next in Weinstein's courtroom came the civil case of alleged sodomy victim Michael Mineo, who claimed he was sexually abused by Police Officer Richard Kern during Mineo's 2008 arrest on a Brooklyn subway platform for smoking marijuana. In February, in a criminal trial, a Brooklyn jury acquitted Kern of sexual abuse and cleared officers Alex Cruz and Andrew Morales of covering up the incident. Mineo has now turned his attention to a $440 million civil suit against the three cops.

In a bizarre twist, their PBA lawyers requested that a fourth cop, John Maloney, who testified against Kern in the criminal trial, become a defendant in the civil case. Weinstein rejected their request, which in another strange twist, Mineo's lawyer, Kevin Mosley, had opposed.

THE SCHIZOPHRENIC POST. The Sunday Post's page one headline: "Massive NYPD shakeup over crime surge." Its story, on page seven, began with: "Facing an alarming surge in murders and other violent crimes..." Police Commissioner Kelly was shifting 40 of his top commanders.

On Page 13, the Post carried another story, headlined, "City's top socialite? NYPD boss Kelly." It began: "The biggest fixture on Manhattan's champagne circuit isn't a Park Avenue princess -- it's Police Commissioner Ray Kelly." The story made no mention of the crime surge. Rather, it said that Kelly "is credited with lowering the crime rate by 20 per cent since his appointment in 2002...."

So should this column call him Top Hat Ray? Or as the Great Breslin referred to former governor Hugh Carey, "Society Kelly?"

NOT THE BIG ONE. The Times Square car bomb that didn't explode may have been a terrorist attack but apparently it was not from Al Qaeda, the Taliban or anyone else in the Mideast. The Nissan Pathfinder that contained the bomb was parked just yards from a military recruiting station, at which, in the middle of the night of March 6, 2008, a bicyclist tossed a small bomb. No one was injured and the center suffered only minimal damage. The bicyclist, who was believed to be an anarchist, was never caught, although police recovered the bicycle.

More interesting, at least to this reporter, the FBI, in a joint news conference at Police Plaza, was represented by George Venizelos, the acting head of the New York office. Absent was its now nominal head, Joe Demarest, who has been in Washington on "special assignment," and possibly suspended, because of a Bureau love indiscretion. Under normal circumstances, Demarest would have returned to New York for such a big event.

Venizelos repeatedly thanked Kelly and chirped the company line about the "seamless" cooperation between the two agencies. A year after the bomb was thrown at the military recruiting station, the NYPD had not turned over the bicycle to the FBI for testing.